Chapter 1.4, Problem 45PPE

To determine

To Evaluate: The expression $\frac{{\left(4\cdot 3\right)}^2}{9+3}$

Answer to Problem 45PPE

The value of expression $\frac{{\left(4\cdot 3\right)}^2}{9+3}$ is $1.5408\overline{3}$

Explanation of Solution

Given:

The expression $\frac{{\left(4\cdot 3\right)}^2}{9+3}$

Concept Used:

To evaluate an expression with different operations, an order needs to be followed. The order is first we open the parenthesis then solve exponents then multiply then divide then add then subtract.

This can be remembered using the word PEMDAS - where P stands for Parenthesis, E stands for Exponents, M stands for Multiplication, D stands for Division, A stands for Addition, S stands for Subtraction.

Calculation:

For the expression $\frac{{\left(4\cdot 3\right)}^2}{9+3}$

  $\begin{array}{c}\frac{{\left(4\cdot 3\right)}^2}{9+3}=\frac{\left(4\cdot 3\right)\times \left(4\cdot 3\right)}{9+3}\text{ Evaluating exponent}\\ =\frac{18.49}{9+3}\\ \text{=}\frac{18.49}{12}\\ =\frac{1849}{1200}\end{array}$

  $=1.5408\overline{3}$

Therefore, the value of expression $\frac{{\left(4\cdot 3\right)}^2}{9+3}$ is $1.5408\overline{3}$

Conclusion:

The value of expression $\frac{{\left(4\cdot 3\right)}^2}{9+3}$ is $1.5408\overline{3}$